Finite Group Databasebeta

← #21458858

Subgroups — #21458858

Order 7808.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840494C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic, complemented
4#16840137C211yesmaximal, characteristic, complemented
5#16839979C211yesmaximal, characteristic, complemented
6#16839974C211yesmaximal, characteristic, complemented
7#16839960C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839954C211yesmaximal, characteristic, complemented
11#16839890C211yesmaximal, characteristic, complemented
12#16839875C211yesmaximal, characteristic, complemented
13#16839874C211yesmaximal, characteristic, complemented
14SD16×Dic61C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×#11758201C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519766C2211yescharacteristic
26#14519763—21no—
27#14519761—21no—
28#14519759—21no—
29#14519749—21no—
30#14519749—21no—
31#14519748—21no—
32Q8×Dic61C2211yescharacteristic
33C4×Dic122C2211yescharacteristic
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic
36D4×Dic61C2211yescharacteristic
37D4×Dic61C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39#14519737—21no—
40#14519709C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#127×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74#11758224—44no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122D411yescharacteristic
80SD16×C61—22no—
81SD16×C61—41no—
82D8×C61—22no—
83D8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758201—41no—
93#11758199—41no—
94#11758199—41no—
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104#11758196D411yescharacteristic
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111D488—22no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117Q8×C61—21no—
118Q8×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—42no—
126D4×C61—81no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C22⋊D61—81no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—81no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150C4×D61—42no—
151C4×D61—81no—
152Dic122—22no—
153C8×C61—21no—
154C8×C61#4112yescomplemented
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61C22×D411yescharacteristic
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61C2×#4111yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183Dic61AGL(1,ℤ/8)12yes—
184#3399—611nomaximal, Sylow
185C2×C61—81no—
186C2×C61—81no—
187C2×C61—81no—
188C2×C61#55011yescharacteristic
189C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C61#57611yescharacteristic
191D61—81no—
192D61—81no—
193#559—611no—
194#550—611no—
195#496—611no—
196#496D6111yescharacteristic, complemented
197#493—611no—
198#463—611no—
199#463—611no—
200#460—611no—
201#459—611no—
202#459—611no—
203#459—611no—
204#446—611no—
205#442—611no—
206#442—611no—
207C4×SD16—611no—
208C61#339911yescharacteristic, complemented, Sylow
209C2×#41—1221no—
210C2×SD16—611no—
211C2×SD16C2×D6111yescharacteristic
212C2×SD16C2×D6111yescharacteristic
213C2×D8—611no—
214C2×D8—611no—
215C2×D8—611no—
216C2×D8—611no—
217C2×D8C2×D6111yescharacteristic
218C2×D8C2×D6111yescharacteristic
219#127—611no—
220#127—611no—
221#127—611no—
222#127C2×D6111yescharacteristic
223#124—611no—
224#124—1221no—
225#124C2×D6111yescharacteristic
226#123—1221no—
227#123—1221no—
228#121—1221no—
229#121—1221no—
230#121—1221no—
231C4×Q8—611no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—611no—
236C4×D4—611no—
237C4×D4—611no—
238C4×D4—1221no—
239#106—611no—
240C4⋊C8—611no—
241C4⋊C8—611no—
242C4⋊C8—611no—
243#103—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#97—611no—
250#97C2×D6111yescharacteristic
251C4×C8—611no—
252#41—2444no—
253C2×Q8—611no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4C22×D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C2×D4C22×D6111yescharacteristic
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273SD16—22no—
274SD16—41no—
275SD16—2441no—
276D8—22no—
277D8—41no—
278D8—1222no—
279D8—2441no—
280D8—2441no—
281D8—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—611no—
302C42—611no—
303C42—1221no—
304C42C22×D6111yescharacteristic
305C23—21no—
306C23—21no—
307C23—21no—
308C23—1221no—
309C23—1221no—
310Q8—21no—
311Q8—21no—
312Q8—1222no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—81no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4—4881no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2442no—
330D4—2442no—
331C2×C4—21no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4D4×D6111yescharacteristic
345C2×C4C23×D6111yescharacteristic
346C8—21no—
347C8—1221no—
348C8—1221no—
349C8#1175822412yescomplemented
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22C2×D4×D6111yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—612no—
370C4—1221no—
371C4—1221no—
372C4—1221no—
373C4—2441no—
374C4—2441no—
375C4C2×#1175822411yescharacteristic
376C4#1451982211yescharacteristic
377C2—81no—
378C2—81no—
379C2—81no—
380C2—4881no—
381C2—4881no—
382C2#1684043211yescharacteristic
383C2AGL(1,ℤ/8)×D6111yescharacteristic
384C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16840494C2semidirect
2. #16840432C2semidirect
3. #16840148C2semidirect
4. #16840137C2semidirect
5. #16839979C2semidirect
6. #16839974C2semidirect
7. #16839960C2semidirect
8. #16839955C2semidirect
9. #16839955C2semidirect
10. #16839954C2semidirect
11. #16839890C2semidirect
12. #16839875C2semidirect
13. #16839874C2semidirect
14. SD16×Dic61C2semidirect
15. C61×#496C2semidirect
154. C8×C61#41semidirect
196. #496D61semidirect
208. C61#3399semidirect
349. C8#11758224semidirect